Playing two words at once in a Scrabble game

Can you build two words in a single turn if you connect to a word that is already there, and then go in the other direction adding to the new word?

Example: The word already on the board is BLAZE (horizontally). On my turn I put -ET on the B to make BET (vertically) and I also put RO- on the T to make ROT (horizontally).

This is all in ONE play. Is it acceptable?

Firstly, just to make sure I understand your example, here is what I believe you mean (and thanks for explaining yourself clearly with an example, by the way!). The letters in the red circled area are all played in a single move...

I'm afraid the answer is a short and sweet NO. The letters you play must all lie in a single row, or a single column, but not both. This has been the rule from the very beginning, and it has never been changed. I've placed a photo of the relevant section of the Scrabble rules from a very old set I own. I've underlined the critical bit.

Sorry to disappoint you ;-)